# Convex side of a thin concavo-convex lens(μ=1.50) has a radius of curvature of 20cm. The concave surface has a radius of curvature 60cm. The concave part is filled with water of μ=1.33 and the convex side is silvered. What is the effective focal length of the optical system?

23 Points
14 years ago

Dear Abhipsa,

We know the lens makers formula...

Now the given case can be considered as combination of

1. A thin lens of Radius of curvatures given by R1= infinity and R2= -60 cm

and μ = 1.33 refractive index of water

it is a thin lens

thus focal length of this lens is f1= 181.81 cm.

2. A concavo convexlength of  R1= -60 and R2= -20 cm

and  μ = 1.5

thus focal length of it for the case of thin lens is f2=60 cm

and

3. A concave mirror of focal length f3= -R/2 = -10 cm

where R= 20cm

thus resultant focal length becomes 1/f = 1/f1 + 1/f2 + 1/f3

as distances between the lenses are zero

thus resultant focal length is -12.85 cm.

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